This invention relates generally to magnetic resonance imaging (MRI), and more particularly the invention relates to three dimensional magnetic resonance imaging using spiral trajectories in k-space.
Magnetic resonance imaging apparatus is widely used in medical diagnosis applications. In very general terms, nuclear magnetic moments are excited at specific spin precession frequencies which are proportional to the local magnetic field. The radio-frequency signals resulting from the precession of the spins are received using pick-up coils. By manipulating the magnetic fields, an array signal is provided representing different regions of the volume. These can be combined to produce a volumetric image of the nuclear spin density of the body.
Referring to the drawing, FIG. 1A is a perspective view partially in section illustrating coil apparatus in a MR imaging system, and FIGS. 1B-1D3illustrate field gradients which can be produced in the apparatus of FIG. 1A. This apparatus is discussed by Hinshaw and Lent, An Introduction to NMR Imaging: From the Block Equation to the Imaging Equation, Proceedings of the IEEE, Vol 71, No. 3, March 1983, pp. 338-350. Briefly, the uniform static field B0 is generated by the magnet comprising the coil pair 10. A gradient field Gx is generated by a complex gradient coil set which can be wound on the cylinder 12. An RF field B1 is generated by a saddle coil 14. A patient undergoing imaging would be positioned along the Z axis within the saddle coil 14.
In FIG. 1B an X gradient field is shown which is parallel to the static field B0 and varies linearly with distance along the X axis but does not vary with distance along the Y or Z axes. FIGS. 1C and 1D are similar representations of the Y gradient and Z gradient fields, respectively.
FIG. 2 is a functional block diagram of the imaging apparatus as disclosed in NMRxe2x80x94A Perspective on Imaging, General Electric Company, 1982. A computer 20 is programmed to control the operation of the NMR apparatus and process FID signals detected therefrom. The gradient field is energized by a gradient amplifier 22, and the RF coils for impressing an RF magnetic moment at the Larmor frequency is controlled by the transmitter 24 and the RF coils 26. After the selected nuclei have been flipped, the RF coils 26 are employed to detect the FID signal which is passed to the receiver 28 and thence through digitizer 30 for processing by computer 20.
The strong static magnetic field is employed to line up atoms whose nuclei have an odd number of protons and/or neutrons, that is, have spin angular momentum and a magnetic dipole moment. A second RF magnetic field, applied as a single pulse transverse to the first, is then used to pump energy into these nuclei, flipping them over, for example to 90xc2x0 or 180xc2x0. After excitation, the nuclei gradually return to alignment with the static field and give up the energy in the form of weak but detectable free induction decay (FID). These D FID signals are used by a computer to produce images.
Magnetic resonance imaging can be planar or two dimensional (2D) or three dimensional (3D). Some of the advantages of using three-dimensional MRI techniques over conventional two-dimensional imaging are that they do not suffer from imperfect slice profiles, and they do not have the same limits for signal-to-noise ratio and spatial resolution. A 3D data set is also conveniently reformatted to allow for new views without the necessity of bringing the patient to the scan room again. Although there are some minor considerations such as storage capacity and processing time, the main reason 3D techniques are not employed more frequently is their long scan times.
Spiral trajectories in k-space have been used in 2D fast imaging. They are especially attractive for the efficiency with which they traverse k-space and for their good properties for flow and motion. See C. Meyer, B. Hu, D. Nishimura and A. Macovski, Magnetic Resonance in Medicine 28, 202-213 (1992). To traverse 3D k-space the spiral trajectory is combined with a projection-reconstruction (PR) rotation. The PR as a trajectory also has good flow and motion insensitivity, since the first moments of the gradients are nulled at the origin. See D. Nishimura, A. Macovski and J. Pauly, IEEE Transactions on Medical Imaging 5, 3 140-151 (1986).
The new trajectories in accordance with the present invention allow faster coverage of k-space, and therefore reduce the total scan time, making 3D MRI more eficient. This has a direct positive impact on cost with respect to the currently used 3D imaging techniques, like 3DFT, and makes 3D imaging available for new applications. This new acquisition strategy presents an advantage over conventional 3DFT even in those situations in which total scan time is not a concern. It gives more flexibility for trading off scan time for SNR.
Briefly, in accordance with the invention, spiral trajectories as used in 2D imaging are selectively employed so that the total scanned areas lie with a three dimensional volume such as a sphere or an ellipsoid or other geometric 3D volume.
In one embodiment of the invention, the trajectory is defined by a 2D planar spiral trajectory that traverses a plane, usually with more than one interleaf, such that the total scanned area is a circle. To get the three dimensional coverage the 2D trajectory is repeated at different rotation angles with respect to an axis in its plane. It is also possible to design the spiral such that the density of 2D coverage is reduced as it approaches the origin. This reduced density will be compensated by the oversampling produced by the rotation of the planes.
In accordance with another embodiment of the invention, planar spiral trajectories are employed to acquire different sections of the sphere or other geometric volume. Since sections which are farther away from the origin need to be smaller, the spirals are slightly different and require a different member of interleaves.
In another embodiment of the invention, k-space is traversed by a trajectory contained in surfaces from conic sections. Such a surface is defined as the surface generated when a line contained in a plane is rotated around an axis. Again, since the surfaces are closer together near the origin, each spiral can be designed such that the distance from turn to turn decreases as the trajectory moves further away from the origin. This compensates for surface separation and generates a more uniform sampling in k-space and also reduces the number of required excitations.
The invention and objects and features thereof will be more readily apparent from the following description and appended claims when taken with the drawings.